14.773 Political Economy of Institutions and Development ...

14.773 Political Economy of Institutions andDevelopment.

Lectures 11-13: Culture, Norms and Institutions

Daron Acemoglu

MIT

March 2021.

Daron Acemoglu (MIT) Political Economy Lectures 11-13 March 2021. 1 / 119

Culture, Norms and Institutions Introduction

What about Culture? Norms?

One view is that economic performance and incentives are partly orlargely shaped by culture, often equated with religious or nationalcultural characteristics determining beliefs, preferences and customs(e.g., Landes or the essays in Harrison and Huntington).

Example:

Europe has more growth-enhancing culture than Africa, northern Italymore than southern Italy etc.

What’s the difference between culture and norms?

Most important challenge: if culture is so important, and veryslow-changing, how do economic incentives and performance changesharply as exemplified by China?



Culture-Institutions Interactions

An alternative, more sophisticated view, is that culture andinstitutions interact, and “culture” is more about social norms thannational cultural characteristics.

Simple examples:

China had an “authority-respecting” culture under Mao and now has amore “individualistic” culture.Or North Korea and South Korea now have very different “cultures”.

A related perspective is that culture and attitudes play some of thesame role as “de facto power” in what has been described so far.

What is the difference between culture and beliefs?

If so, “culture” could be a mechanism for persistence or even anautonomous force affecting how society is organized.

Equally importantly, if so, we should really study the determinants ofcultural change (or better, changes in social norms).



Culture-Institutions Interactions

Perhaps

culturet =⇒ economic performancet =⇒ culturet+1

Or

politicalinst’st

culturet

=⇒ econ.inst’st

=⇒

econ. perft

culturet+1

political inst’st+1



Evidence on Effect of Culture

Plenty of correlation evidence and several studies showing historicaleffects, but sometimes diffi cult to interpret.

Tabellini (2008): use differences in constraints on executive across asubnational units (within current nations) in the past, as aninstrument for contemporary culture variables (in particular,generalized vs. clan or family-based trust, as in Banfield).

Identification assumption: constraints on the executive in the distantpast to not have a direct effect. Is this plausible? Tabellini argues yesbecause there are country fixed effects. But potentially, no ifinstitutions persist at the local level.

Guiso, Sapienza and Zingales (2009) and Fernandez and Fogli (2009)show that certain behavioral patterns (e.g., fertility and women’slabor supply) of second or third generation immigrants are highlycorrelated with these variables in their country of origin. They arguethat the channel must be cultural.



Evidence on Effect of Culture (continued)

Tabellini (2008): relationship between generalized trust and incomeper capita




Potentially working through institutions



Interpretation

What could be interpretation be?

Threat to validity:

is what persists culture?is culture adapting or driving?




Fernandez and Fogli (2009) persistent effects of culture on values andbehavior



Interpretation

What persists from home country to the United States?

Threats to validity:

Do second-generation immigrants from different countries live undersimilar circumstances? Are they fully integrated?In the same or different neighborhoods?Are they subject to the same labor market opportunities (because ofdiscrimination or externalities)?

Is this culture, norms or something else? Social organization?Neighborhoods?




Guiso, Sapienza and Zingales: bilateral trust as a function of religiousand genetic overlap (why?)




Export from country i to j on trust of country j to i




FDI from country i to j on trust of country i to j



Interpretation

History vs. culture/trust.

Reverse causality.

What does genetic and religious distance capture?



Overall Interpretation

While there are potential issues with any single study on institutionsand on culture, in both cases the body of evidence probably suggeststhat these regressions are capturing something real.

Interpretation is in general open and needs to be done in light ofsome theoretical and historical ideas.


Culture, Norms and Institutions Intergenerational Transmission of Values

Introduction

How do we model the effects of culture and values on social andpolitical outcomes– and through which mechanisms?

Why do these values persist?

How they interact with institutions?

In this lecture, an overview of some related research.



Intergenerational Transmission: Basic Models

Cavalli-Sforza and Feldman (1981) and to Boyd and Richerson(1985), based on models of evolutionary biology applied to thetransmission of cultural traits.

Suppose that there is a dichotomous cultural trait in the population,{a, b}. Let the fraction of individuals with trait i ∈ {a, b} be qi .Focus on a continuous time model with “a-sexual”reproduction whereeach parent has one child at the rate λ and is replaced by the child.

Two types of cultural transmission:1 direct/vertical (parental) socialization and2 horizontal/socialization by the society at large.



Intergenerational Transmission (continued)

Suppose that direct vertical socialization of the parent’s trait, say i ,occurs with probability d i .

Then, if a child from a family with trait i is not directly socialized,which occurs with probability 1− d i , he/she is horizontally/obliquelysocialized by picking the trait of a role model chosen randomly in thepopulation (i.e., he/she picks trait i with probability qi and trait j 6= iwith probability qj = 1− qi ).Therefore, the probability that a child from family with trait i issocialized to have trait j , P ij , is:

P ii = d i + (1− d i )qi

P ij = (1− d i )(1− qi ). (1)




Now noting that each child replaces their parent in the population (atthe rate λ), we have that

qi = λ[(d i + (1− d i )qi

)qi + (1− d j )qi

(1− qi

)]− λqi .

Simplifying this equation, we obtain:

qi = λqi (1− qi )(d i − d j

). (2)

This is a version of the replicator dynamics in evolutionary biology fora two-trait population dynamic model– i.e., a logistic differentialequation.If(d i − d j

)> 0 cultural transmission represents a selection

mechanism in favor of trait i , due to its differential verticalsocialization.However, this selection mechanism implies that there will not becultural heterogeneity, i.e., a steady-state with 0 < qi∗ < 1.




The following result is now immediate.

Let qi (t, qi0) denotes the fraction with trait qi at time t starting with

initial condition qi0. Then:

Proposition

Suppose d i > d j . Then, steady states are culturally homogeneous.Moreover, for any qi0 ∈ (0, 1], qi (t, qi0)→ 1. If instead d i = d j , thenqi (t, qi0) = q

i0, for any t ≥ 0.



Intergenerational Transmission: Bisin-Verdier Model

Bisin and Verdier (2000, 2001) introduce “imperfect empathy” intothis framework, whereby parents look at the world with their ownpreferences and thus wants to socialize their offspring according totheir preferences.

Formally, suppose that individuals choose an action x ∈ X tomaximize a utility function ui (x), which is a function of the culturaltrait i ∈ {a, b}. Suppose that this utility function is strictlyquasi-concave.




Let V ij denote the utility of a type i parent of a type j child,i , j ∈ {a, b}. Then clearly, we have

V ij = ui (x j )

Andx j = argmax

x∈Xuj (x)

This implies the “imperfect empathy” feature:

V ii ≥ V ij

holding with > for generic preferences (i.e., in particular when themaximizers for the two types are different).




Suppose also that parents have to exert costly effort in order tosocialize their children. In particular, parents of type i choose somevariable τi , which determines

d i = D(qi , τi

).

The dependence on q captures other sources of direct transmissionworking from the distribution of traits in the population.The cost of τi is assumed to be C

(τi).

Suppose that D is continuous, strictly increasing and strictly concavein τi , and satisfies D

(qi , 0

)= 0, and C is also continuous, strictly

increasing and convex. Moreover, suppose also that D(qi , τi

)is

nonincreasing in qi .Parents of type i will solve the following problem:

maxτi−C (τi ) + P iiV ii + P ijV ij ,

where P ii and P ij depend on τi via d i .Daron Acemoglu (MIT) Political Economy Lectures 11-13 March 2021. 24 / 119



Let us say that the cultural substitution property holds if the solutionto this problem d i∗ is is strictly decreasing function of qi and takes avalue d i∗ = 0 at qi = 1. Intuitively, this implies that parents have lessincentives to socialize their children when their trait is morepopular/dominant in the population.This cultural substitution property is satisfied in this model.Then, the dynamics of cultural transmission can be more generallywritten as

qi = λqi (1− qi )(d i(qi)− d j

(1− qi

)). (3)

We can also verify that this differential equation has a unique interiorsteady state, qi∗, and moreover,

Proposition

The steady states are now culturally heterogeneous. In particular,qi (t, qi0)→ qi∗, for any qi0 ∈ (0, 1).




Intuition: the cultural substitution property implies that parents putmore effort in socializing their children, i.e., passing on their traits,when their traits are less common in the cooperation.

The proof of this result follows from the following observations:1 Clearly, an interior steady state satisfies

d i(qi)− d j

(1− qi

)= 0,

and since both d i and d j are strictly decreasing, there can at most beone such steady state qi∗.

2 Moreover, since d i (1) = 0, existence is guaranteed.3 Global stability then follows from the fact that this pattern implies thatqi > 0 whenever qi ∈

(0, qi∗

)and at qi < 0 whenever qi ∈

(qi∗, 1

).


Culture, Norms and Institutions Culture and Cooperation

Culture, Values and Cooperation

Tabellini (2009) considers the following variation on the staticprisoners’dilemma game.

Individuals incur a negative disutility from defecting, but the extent ofthis disutility depends on how far their partner is according to somedistance metric.

The most interesting interpretations of this distance are related to“cultural distance”or “kinship distance”. For example, someindividuals may not receive any disutility from defecting on strangers,but not on cousins.This captures notions related to “generalized trust”.



Model

A continuum of one-period lived individuals, with measure normalizedto 1, is uniformly distributed on the circumference of a circle of size2S , so that the maximum distance between two individuals is S .

A higher S implies a more “heterogeneous” society– in geography,ethnicity, religion or other cultural traits.

Each individual is (uniformly) randomly matched with another locatedat distance y with probability g(y) > 0, and naturally∫ S

0g(y) = 1.



Model (continued)

A matched pair play the following prisoners’dilemma:

C DC c , c h− l , c + wD c + w , h− l h, h

Naturally, c > h and l ,w > 0. Let us also suppose that l ≥ w , sothat the loss of being defected when playing cooperate is no less thanthe reverse benefit.



Model (continued)

In addition, each individual enjoys a non-economic (psychological ormoral) benefit

de−θy

whenever she plays “cooperate” (regardless of what her opponentplays) but as a function of the distance between herself and the otherplayer, y , with the benefit declining exponentially in distance.

Let us assume thatd > max{l ,w},

which ensures that this benefit is suffi cient to induce cooperation withpeople very close.



Model (continued)

Finally, suppose that there are two types of player indexed byk = 0, 1, “good”and “bad,”modeled as having different rates atwhich the benefit from cooperation declines. In particular,

θ0 > θ1.

This captures the idea that what varies across individuals (andperhaps across societies) is the level of “generalized trust”.

The fraction of good (k = 1) types in the population is the same atany point in the circle is 1 > n > 0.



Equilibrium

Consider a player in a match of distance y .

Let π(y) denote the probability that her opponent will play C .

We can express the player’s net expected material gain from defectinginstead of laying C as:

T (π(y)) = [l − π(y) (l − w)] > 0 (4)

This is strictly positive, as it is always better not to cooperate giventhe prisoners’dilemma nature of the game.

Note also that cooperation decisions are strategic complements, since,given the assumption that l ≥ w , the function T (π(y)) isnon-increasing in π(y)



Equilibrium (continued)

The temptation to defect will be potentially balanced by thenon-economic benefit of cooperation, de−θk y , as a function of aplayer’s type.To simplify the analysis, let us suppose that

θ0

θ1>ln(l/d)ln(w/d)

(A0)

and also focus on “best” (Pareto superior) and symmetric(independent of location on the circle) equilibria.Then a player of type k = 0, 1 will be indifferent between cooperatingand not cooperating with a partner of distance y k defined as

T (π(y k )) = de−θk y k , (5)

Or asy k =

{ln d − ln

[(w − l)π(y k ) + l

]}/θk . (6)




Thus given the equilibrium probability of cooperation π(y) (for all y),each individual will cooperate with players closer than y k (y < y k )and defect against those farther than y k as a function of her type k.

Note that if l > w , then the right hand side of (6) is increasing inπ(y), and there are multiple equilibria, though we are ignoring this byfocusing on best equilibria.

Now consider a bad player, k = 0, and suppose that she/he expectsthe opponent always to cooperate, so that π(y) = 1 (which will betrue, since both types of players will cooperate whenever this player ischoosing to operate along the equilibrium path).

Then (6) reduces to:

Y 0 = [ln d − lnw ] /θ0, (7)

and player k = 0 will cooperate up to distance y ≤ Y 0.Daron Acemoglu (MIT) Political Economy Lectures 11-13 March 2021. 34 / 119



The problem of a good player is a little more complicated.

She will necessarily cooperate up to distance y ≤ Y 0. But beyondthat, she recognizes that only other good players will cooperate, andthus π(y) = n.

Using this with (6)

Y 1 = [ln d − ln [(w − l) n+ l ]] /θ1. (8)

And with players cooperate up to Y 1 (which is strictly greater thanY 0 given the assumption above).




Thus summarizing:

Proposition

In the Pareto superior symmetric equilibrium, a player of type k cooperatesin a match of distance y ≤ Y k and does not cooperate if y > Y k , whereY k is given (7)-(8), for k = 0, 1.

This proposition captures, in a simple way, the role of “generalizedtrust” in society.

It also highlights the strategic complementarity in trust, as Y 1 isincreasing in n: thus good players trust others more when there aremore good players. Interestingly, this does not affect bad types, giventhe simple structure of the prisoners’dilemma game coupled with theassumption that l ≥ w .



Endogenous Values

Values can now be endogenized using the same approach as Bisin andVerdier.

Parents choose socialization effort τ at cost

12ϕ

τ 2,

and as a result, their offspring will be over the “good type,” i.e.,θk = θ1, with probability δ+ τ .

As in Bisin and Verdier, they evaluate this with their own preferences,i.e., there is “imperfect empathy”.



Endogenous Values (continued)

Let V pkt denote the parent of type p’s evaluation of their kid of typek’s overall expected utility in the equilibrium of the matching game.Since the probability of a match with someone located at distance zis denoted g(z), we have

V pkt = Ukt + d

Y kt∫0

e−θpzg(z)dz , (9)

where Ukt = U(θk , nt ) denotes the expected equilibrium material

payoffs of a kid of type k, in a game with a fraction nt of goodplayers. The integral gives the parent’s evaluation of their kid’sexpected non-economic benefit from their offspring’s cooperating inmatches of distance smaller than Y kt .This is where imperfect empathy comes in, as this integral term usesthe parent’s value parameter, θp , rather than with the kid’s value.




With the same argument as in Bisin and Verdier, we have thatwhenever k 6= p, then

V ppt > V pkt

where recall that, given the assumptions, Y 1 > Y 0.

The fact that parents of bad type, according to their values, havenothing to gain from exerting effort to socialize their children to begood (as they do not internalize the “moral”benefit from cooperationwith farther away partners), and the fact that the marginal cost ofexerting effort at zero is zero, implies the following simple result:

Proposition

A “good" parent (p = 1) exerts strictly positive effort τt > 0. A “bad"parent (p = 0) exerts no effort.




Therefore, the law of motion of types in the population follows thefollowing difference equation:

nt = nt−1(δ+ τt ) + (1− nt−1)δ = δ+ nt−1τt . (10)

It can also be shown that the optimal level of effort for with typeparents is τt = F

(Y 1t), where

F(Y 1t)≡ ϕd [−e−θ1Y 1t +E [e−θ1y | Y 1t ≥ y ≥ Y 0]]Pr(Y 1t ≥ y ≥ Y 0),

(11)where intuitively the benefit to good parents depends on thelikelihood that their children will play against an opponent of goodtype, again highlighting the strategic complementarities. Theright-hand side of (11), F (Yt ), is as a result strictly increasing in Y 1t .




This means that (10) can be written as

nt = δ+ nt−1F (Y 1t ) ≡ N(Y 1t , nt−1), (12)

with the date t equilibria value of Y 1t being defined as:

Y 1t = [ln d − ln [(w − l) nt + l ]] /θ1 ≡ Y (nt ).

Now using the fact that nt itself is a function of nt−1 and Y 1t from(10), we can express endogenous value dynamics as in two equationssystem:

Y 1∗t = GY (nt−1) (13)

n∗t = G n(nt−1) (14)

Strategic complementarities now imply multiple steady state arepossible.




Naturally, additional conditions ensure uniqueness. One suchcondition would be

1ϕ> l − w (A1)

which ensures that the marginal cost of effort, 1/ϕ, rises suffi cientlyrapidly, relative to the strategic complementarity captured by (l −w).Given uniqueness, global stability of dynamics can also be ensured.The following proposition gives one suffi cient condition

Proposition

Suppose (A1) holds and ϕ > 0 is suffi ciently small. Then the equilibriumis unique and is globally stable, i.e., it asymptotically reaches the uniquesteady state (Y 1∗s , n

∗s ). Moreover, adjustment to steady state is monotone,

i.e., the fraction of what types, n∗t , and the cooperation threshold, Y1∗t ,

andmonotonically increase or decrease along the adjustment path.



Effects of Institutions

Let us introduce institutional enforcement of cooperation simply byassuming that there is a probability χ(y) that defection gets detectedwhen it takes place in a match of distance y and it gets punished.We can think of different types of shifts up the schedule χ (y) ascorresponding to different types of changes in institutions.In particular, we can imagine that χ increases for high y . This willencourage more broad-based cooperation and it will also incentivizeparents to socialize their children to be of the “good” type. As aresult, both n∗t and Y

1∗t will increase.

At the other extreme, we can think of an improvement in localenforcement, with no change in enforcement for faraway matches.This could be considered as a family- or clan-based enforcement, orwhat the Mafia achieves in southern Italy. This would increase Y 0, soits static effect is good. However, it would also reduce the parentalefforts for good socialization, so ultimately it would reduce n∗t andY 1∗t .



Endogenous Institutions

One could also endogenize enforcement through a voting or politicaleconomy process.

In this case, one can obtain richer dynamics, where parentalsocialization interacts with political economy. For example, more withtypes today leads to greater enforcement, which then encouragesmore would socialization.

Multiple steady states are again possible, this time resulting from theinteraction of culture and institutions.


Culture, Norms and Institutions An Alternative Framework for Culture

An Alternative Framework

But perhaps this way of thinking about culture– as largelyunchanging, and good vs. bad– is not very helpful.

Let’s think of a different approach (based on Acemoglu and Robinson,2021) centered on the interplay between social equilibria(representing the ensemble of political, economic and socialarrangements) and cultural configurations (representing culturalconstraints as we will describe next).

Social equilibria and cultural configurations are jointly determined.

But in some instances it will be political, economic and otherenvironmental factors that shape cultural configurations, and yet inothers, it will be cultural configurations that fundamentally constrainsocial equilibria.



Culture Set, Attributes and Cultural Configurations

We view culture as a set of beliefs, relationships, rituals andobligations that provide a framework to people to interpret the world,coordinate expectations and constrain behaviors.

In contrast to the approaches that assume that cultures correspond tostable values, we argue that a culture is defined by a culture set,containing a number of distinct (cultural) attributes.Example attributes include: definitions of distinct groups in society;types of social hierarchy; various social responsibilities; familystructures; specific rituals (such as witchcraft or ancestor worship);interlocking set of obligations (from parents to children or fromregular people to elites); and certain higher ideals (such as differenttypes of virtue or honor, importance of order or in society, or values ofequality or hierarchy and status).

A cultural configuration is created from combinations of subsets ofattributes in a culture set.



Multitudes of Cultural Configurations

Crucially, the attributes in the culture set (except in uniquely rigidcultures) can be combined to support a multitude of feasible culturalconfigurations.

For example, social hierarchy could be one in which rulers or certainprivileged groups have to be obeyed all the time, or it may include thenotion that, as in Confucian culture, virtuous leaders should beobeyed.

The former, especially if it is rigidly specified, may take the form of acaste-based society (literally and figuratively).

The latter can on the other hand allow different types of social andpolitical organizations.



Social Equilibria and Cultural Configurations

So what determines which cultural configuration is realized?

Our framework is predicated on the notion that this is jointlydetermined with the social equilibrium.

If political power lies in the hands of a narrow group that can wieldthis power in order to shape the social equilibrium, a culturalconfiguration that justifies this type of social equilibrium may arise (ifit is feasible).

But under other circumstances, a very different cultural configurationmay arise as part of the social equilibrium.

Our discussion below of how Confucian culture has supported Imperialinstitutions, Communist Party rule and democracy in Taiwan andHong Kong (and South Korea) will illustrate these ideas.



Cultural Constraints

However, our framework does not imply that cultures are perfectlymalleable, adapting to political power, economic conditions or otherenvironmental factors.

The set of cultural configurations that a culture allows will be, by itsnature, finite.

This means that certain social equilibria will be ruled out (unless theculture can fundamentally change– more on this below).

This will be all the more so when a culture is hardwired.For example, as we discuss next, the Indian caste system and theculture set that it is associated with severely constrain economic andpolitical arrangements if they conflict with the pre-ordained hierarchyof groups.



Fluid and Hardwired Cultures

We say that a culture is more fluid than another if it has attributesthat can be combined in more distinct ways and thus allow for alarger set of cultural configurations.

By this definition, a fluid culture will allow the formation of morediverse cultural configurations and as a result will be less constrainingfor social equilibria than a hardwired culture.

Put differently, a hardwired culture is more likely to be one wherecultural configuration act as hard constraints on political, social andeconomic arrangements.



Culture and Social Equilibria

In principle, cultural configurations and social equilibria are jointlydetermined– meaning that politics, economic outcomes and socialrelations shape as much as being shaped by cultural configurations.

The exception to this is the polar case of extremely hardwired culturesthat allow only very limited cultural configurations.

This gives an extreme special case of our framework corresponding to“vulgar culturalism”, where everything is shaped by an unchanging(hugely persistent) culture.



Cultural Configurations and Social Equilibria under anExtreme Hardwired Culture

Institutions do not affect culture and politics is absent.We have not dwelt on the green arrows which may also be present(the culture set directly impacting institutions, e.g., via languageetc.).



Cultural Configurations and Social Equilibria in General

Institutions affect culture and politics (and other environmentalfactors) now play a central role. Culture still plays a role, but in amore limited way, since cultural configurations are adaptable to socialconditions and political factors.



Understanding Fluid and Hardwired Cultures

So what makes a culture more fluid or more hardwired?In practice, many factors play a role, but our analysis focuses on twofeatures of its attributes as represented by the next table:

abstract specificfree standing fluid culture intermediate cultureentangled intermediate culture hardwired culture

Diagonals are most common and easier to study, but there are someinteresting phenomena in off-diagonals as well, as we will discuss.Note that there should be no expectation that hardwired cultures willautomatically lead to worse social equilibria. The hardwired culturalconfigurations may be those that favor economic or politicaldevelopment (at least under some circumstances).



Abstract versus Specific Attributes

We say that an attribute is abstract if it can be combined withdifferent attributes in different ways.

On the other hand, it is specific if it narrowly specifies the prescribedroles and/or values and behaviors.

Because abstract attributes can be combined with others in manydifferent ways, they can be reinterpreted when the social equilibriumor other pressures demand such a change.

This implies that when attributes are more specific, the set of feasiblecultural configurations will be more limited.

A common attribute, present in many culture sets, is a type ofin-group social hierarchy: the in-group can or should be treated betterthan the out-group.

But this can be either abstract or specific as we next discuss.



Abstract vs. Specific Attributes in Islamic and BritishCultures

In Islam this social hierarchy attribute is specific: Muslims are thein-group.The Quran decrees (9.29):Fight those of the People of the Book who do not [truly] believe inGod and the Last Day, who do not forbid what God and hisMessenger have forbidden, who do not obey the rule of justice, untilthey pay the tax and agree to submit.“The tax” (jizya) was interpreted as a poll tax on non-Muslims (thePeople of the Book– Jews and Christians) later specified to be 48dirhams for the rich, 24 for the middle incomes and 12 for the poorer.Compare this to Britain. Before the Reformation being Catholic wasone identifier of the in-group, heretics were the persecuted out-group.By Elizabethan times and for 250 years until Catholic Emancipationin 1829 Catholics became the out-group. They paid higher taxes,their lands could be forfeit, and they could not hold public offi ce.But the attributes in Britain were abstract and did not specify whowas the in-group and the out-group so this could change over time.



Entangled versus Free-Standing Attributes

We say that an attribute is entangled if its form or function is tightlylinked to other attributes in the culture set, limiting how it can becombined with different combinations of other attributes.

It is free standing if it is independent from other attributes and canbe more easily combined with others or sidelined.

Entangled attributes can be combined with others in more limitedways, thus reducing the range of cultural configurations that arefeasible.



Entangled vs. Free-Standing Attributes in Islam and Britain

Returning to the issue of social hierarchy, another key differencebetween the Islamic and British case is that in Islam, discriminationagainst non-Muslims was part of the Sharia.

The Sharia is the law of God revealed by the Archangel Gabriel toMohammed and as such cannot be changed by legislation (like theCatholic Emancipation Act).

Thus the distinction between the in-group and out-group in Islamicculture is not just more specific, it is also entangled with otherattributes, here religious beliefs.

In Britain, the identities of in-group and out-group were freestanding and thus relatively amenable to change.



Evolution of Cultures

Our framework building on properties of attributes in a culture set(rather than the nature and precepts of an unchanging,all-encompassing culture) may also be useful in providing newperspectives on why cultural attributes vary in the degree to whichthey are specific, abstract, and entangled and free standing.Hayek famously claimed in The Constitution of Liberty that evolvedinstitutions and cultures were superior to those that resulted fromradical changes.But the reason for this is still unclear (and the empirical validity ofthis claim can also be questioned).The issue of empirical reach of this claim notwithstanding, ourframework suggests one reason why evolved cultures may have somedesirable properties:

gradual evolution of cultures would make it unlikely that they have veryspecific and entangled attributes, thus helping them become more fluidover time.



Off-Diagonal Attributes

Entangled and specific attributes seem to travel together, but thereare cases of intermediate cultures, with entangled and abstractattributes or free-standing and specific attributes.Witchcraft plays an important role in the culture sets of many Africancultures.

It can be construed as an example of an entangled and abstractattribute, since it can be evoked as an explanation for more or lessanything (illness, set-backs, economic or political success (or failure)),but it is quite malleable and witchcraft can be directed towardspowerful politicians, rich individuals or regular people and accusationsof sorcery can be made by anyone.

Anti-Jewish customs and beliefs in medieval Europe could be viewedas an example of a specific but free-standing attribute.

They are clearly very specific (they cannot be easily directed againstother groups or turned into practices friendly to Jews).But they are not closely entangled with other customs, beliefs andvalues.



Cultural Collapse

So what happens when a hardwired culture is confronted bycircumstances that are incongruent with any of the culturalconfigurations that it can support?

One possibility is that the hardwired culture will tend to survive andinduce a cultural configuration that forces an ineffi cient socialequilibrium.

However, another possibility is one of cultural collapse– either theculture abandoning some of its attributes (and adding new ones) ormany people leaving the culture (for example in the form of religiousconversions).

One obvious implication is that cultural collapse is more likely to bethe case for hardwired cultures– which could be good or bad foreconomic or political development.



Cultural Persistence

How do we think about cultural persistence in our framework?

Several new ideas arise from what we have presented already.

First, many aspects of cultures will tend to persist precisely becausethey do not constrain economic, social or political behavior (forexample cuisine or non-economic, non-political rituals).

Second, more fluid cultures will tend to persist more because they canadapt to changing circumstances by generating new culturalconfigurations– but paradoxically, these are also the cultures that arechanging more in the sense of generating distinct culturalconfigurations. But this is despite the fact that they are using thesame attributes and hence appear to rely on the same “values”.

Third, cultures will persist and tend to be defining for the nature ofsocial equilibria when they are hardwired and can withstand forcestowards cultural collapse.


Culture, Norms and Institutions Endogenous Norms of Corporation

Endogenous Norms of Cooperation

Different focus: how does “cooperation” (or “solution to collectiveaction problem”) emerge, and why does “history”affect the outcomeof such cooperation games? How and why do norms of corporationchange?

Why does a history of distrust leads to distrust? How do weunderstand “social norms”and why do they persist?Why does a society sometime break out of a history of distrust andchange social norms?Why does “collective action”differ across societies and why does itseem to change abruptly from time to time?What is the role of leadership and “prominence”?

Simple model based on Acemoglu and Jackson (2011).



Model

Consider an overlapping-generations model where agents live for twoperiods. We suppose for simplicity that there is a single agent in eachperiod (generation), and each agent’s payoffs are determined by hisinteraction with agents from the two neighboring generations (olderand younger agents).

The action played by the agent born in period t is denotedAt ∈ {H, L}, corresponding to “High”and “Low”actions (also canbe interpreted as “honest” and “dishonest”actions).

An agent chooses an action only once, in the first period of his or herlife and that is played in both periods. This can be thought of as aproxy for a case where there is discretion, but also a high cost ofchanging behavior later in life.



Model

The stage payoff to an agent playing A when another agent plays A′

is denoted u(A,A′). The total payoff to the agent born at time t is

(1− λ) u(At ,At−1) + λu(At ,At+1), (15)

where At−1 designates the action of the agent in the previousgeneration and At+1 is the action of the agent in the next generation.

Implicit assumption: choose single “pattern of behavior”At againstboth generations

λ ∈ [0, 1] is a measure of how much an agent weighs the play with thenext generation compared to the previous generation.

When λ = 1 an agent cares only about the next generation’s behavior,while when λ = 0 an agent cares only about the previous generation’sactions. We do not explicitly include a discount factor, since it issubsumed by λ.



Demographics



Model (continued)

The stage payoff function u(A,A′) is given by the following matrix:

H LH β, β −α, 0L 0,−α 0, 0

where β and α are both positive.

This payoff matrix captures the notion that, from the static point ofview, both honesty and dishonesty could arise as social norms– i.e.,both (H,H) and (L, L) are static equilibria given this payoff matrix.(H,H) is clearly the Pareto optimal equilibrium, and depending onthe values of β and α, it may be the risk dominant equilibrium as well.



Endogenous and Exogenous Agents

There are four types of agents in this society.

First, agents are distinguished by whether they choose an action tomaximize the utility function given in (15). We refer to those who doso as “endogenous”agents.

In addition to these endogenous agents, who will choose theirbehavior given their information and expectations, there will also besome committed or “exogenous”agents, who will choose anexogenously given action.

This might be due to some irrationality, or because some agents have adifferent utility function.



Endogenous and Exogenous Agents (continued)

Any given agent is an “exogenous type”with probability 2π(independently of all past events), exogenously committed to playingeach of the two actions, H and D, with probability π ∈ (0, 12 ), andthink of π as small.With the complementary probability, 1− 2π > 0, the agent is“endogenous”and chooses whether to play H or D, when young andis stuck with the same decision when old.Any given agent is also “prominent”with probability q (againindependent). Information about prominent agents will be different.Thus:

non-prominent prominentendogenous (1− 2π) (1− q) (1− 2π) qexogenous 2π (1− q) 2πq

Let us refer to endogenous non-prominent agents as regular.



Signals, Information and Prominent Agents

A noisy signal of an action taken by a non-prominent agent ofgeneration t is observed by the agent in generation t + 1.

No other agent receives any information about this action.

In contrast, the actions taken by prominent agents are perfectlyobserved by all future generations.



Information Structure

Let ht−1 denotes the public history at time t, which includes a list ofpast prominent agents and their actions up to and including timet − 1. We denote the set of ht−1 histories by Ht−1.We write ht = (T , a) if at time t the agent is both prominence typeT ∈ {P,N} and has taken action a ∈ {H, L} if T = P (if T = N,his action is not part of the public history).

In addition to observing ht−1 ∈ Ht−1, an agent of generation t, whenborn, receives a signal st ∈ [0, 1] about the behavior of the agent ofthe previous generation (where the restriction to [0, 1] is without lossof any generality). This signal has a continuous and distributiondescribed by a density function fH (s) if At−1 = H and fL (s) ifAt−1 = L.



Information Structure (continued)

Without loss of generality, we order signals such that higher s has ahigher likelihood ratio for H; i.e., so that

g (s) ≡ fL(s)fH (s)

is nonincreasing in s.Suppose also that it is strictly decreasing, so that we have strictMonotone Likelihood Ratio Property (MLRP) everywhere.Suppose, without loss of any generality, that s ∈ [0, 1], so that 0 isthe worst signal for past H and 1 best signal for past H.Let Φ (x , s) denote the posterior probability that At−1 = H givenst = s under the belief that an endogenous agent of generation t − 1plays H with probability x . This is:

Φ (x , s) ≡ fH (s) xfH (s) x + fL (s) (1− x)

=1

1+ g (s) 1−xx. (16)

The game begins with a prominent agent at time t = 0 playingA0 ∈ {H, L}.Daron Acemoglu (MIT) Political Economy Lectures 11-13 March 2021. 72 / 119


Strategies

Let us use N to denote regular agents and P to denote prominentagents.

With this notation, we can write the strategy of an endogenous agentof generation t (who may or may not be regular) as:

σt : Ht−1 × [0, 1]× {P,N} → [0, 1],

written as σt (ht−1, s,T ) where ht−1 ∈ Ht−1 is the public history ofplay, s ∈ [0, 1] is the signal of the previous generation’s action, andT ∈ {P,N} denotes whether or not the current agent is prominent.The number σt (s, ht ,T ) corresponds to the probability that theagent of generation t plays H.

We denote the strategy profile of all agents by the sequence

σ =(σ1(h0, s,T ), σ2(h1, s,T ), ..., σt (ht , s,T ), ...

).



Semi-Markovian Strategies

For the focus here, the most relevant equilibria involve agentsignoring histories that come before the last prominent agent (inparticular, it will be apparent that these histories are notpayoff-relevant provided others are following similar strategies).Let us refer to these as semi-Markovian strategies.Semi-Markovian strategies are specified for endogenous agents asfunctions σSMτ : {H,D} × [0, 1]× {P,N} → [0, 1], written asσSMτ (a, s,T ) where τ ∈ {1, 2, . . .} is the number of periods since thelast prominent agent, a ∈ {H,D} is the action of the last prominentagent, s ∈ [0, 1] is the signal of the previous generation’s action, andagain T ∈ {P,N} is whether or not the current agent is prominent.Let us denote a semi-Markovian by the sequenceσSM =

(σSM1 (a, s,T ), σSM2 (a, s,T ), ..., σSMt (a, s,T ), ...

).

With some abuse of notation, write σt = H or D to denote a strategy(or a semi-Markovian strategy) that corresponds to playing honest(dishonest) with probability one.



Equilibrium Definition

Perfect Bayesian Equilibrium or Sequential Equilibrium.

Only need to be careful when q = 0.

Define greatest and least equilibria, and focus on greatest equilibria.



Towards Equilibrium Behavior

Let φtt−1 be the the probability that the agent of generation t assignsto the agent from generation t − 1 choosing A = HLet φtt+1 be the probability that the agent of generation t assigns,conditional on herself playing A = H, to the agent from generationt + 1 choosing A = H.Payoff from L: 0Payoff from H:(1− λ)

[φtt−1β− (1− φtt−1)α

]+ λ

[φtt+1β− (1− φtt+1)α

].

Then an endogenous agent of generation t will prefer to play A = Honly if

(1− λ) φtt−1 + λφtt+1 ≥α

β+ α≡ γ. (17)

Parameter γ a convenient way of summarizing relative payoffs (andalso “basin of attraction”of L; so the greater is γ, the moreattractive it is A = L).



Cutoff Strategies

We say that a strategy σ is a cutoff strategy if for each t, ht−1 suchthat ht−1 = N and Tt ∈ {P,N}, there exists s∗t such thatσt (ht , s,Tt ) = 1 if s > s∗t and σt (ht , s,Tt ) = 0 if s < s∗t .

Clearly, setting σt (ht , s,T ) = 1 (or 0) for all s is a special case of acutoff strategy.

Cutoff strategy profile can be represented by the sequence of cutoffs

c =(cN1 (h0), c

P1 (h0), ...c

Nt (ht−1), c

Pt (ht−1), ...

).

Given strict MLRP, all equilibria will be in cutoff strategies.

Define greatest equilibria using the Euclidean distance on cutoffs.



Equilibrium Characterization

Proposition

1 All equilibria are in cutoff strategies.2 There exists an equilibrium in semi-Makovian cutoff strategies.3 The set of equilibria and the set of semi-Markovian equilibria formcomplete lattices, and the greatest (and least) equilibria of the twolattices coincide.



Understanding History-Driven Behavior

Look for a unique equilibrium given by history:

When following prominent H, will all endogenous agents play H?When following prominent L, will all endogenous agents play L?

In such an equilibrium, social norms of High and Low emerge andpersist, but not forever, since there might be switches because ofexogenous prominent agents.

Related question: when is this the greatest equilibrium?



Understanding History-Driven Behavior (continued)

Recall that an endogenous agent of generation t will prefer to playA = H only if

(1− λ) φtt−1 + λφtt+1 ≥α

β+ α≡ γ. (18)

H is a unique best response for all if

(1− λ) φtt−1 + λφtt+1 ≥ γ

γ∗H ≡ (1− λ)Φ (1− π, 0) + λπ ≥ γ.

L is a unique best response for all if

(1− λ) φtt−1 + λφtt+1 < γ

γ∗L ≡ (1− λ)Φ (π, 1) + λ(1− π) < γ.




Proposition

1 If γ < γ∗H , then following a = H at date t = 0, the uniquecontinuation equilibrium involves all (prominent and non-prominent)endogenous agents playing H.

2 If γ > γ∗L, then following a = L at date t = 0, the uniquecontinuation equilibrium involves all endogenous agents playing L.

3 If γ∗L < γ < γ∗H , then there is a unique equilibrium driven by thestarting condition: all endogenous agents take the same action as theaction of the prominent agent at date t = 0.

Interpretation: persistent, but not everlasting, social norms.




The condition that γ∗L < γ < γ∗H boils down to

λ(1− 2π) < (1− λ) [Φ(1− π, 0)−Φ(π, 1)] . (19)

It requires that λ be suffi ciently small, so that suffi cient weight isplaced on the past. Without this, behavior would coordinate withfuture play, which naturally leads to a multiplicity.

It also requires that signals are not too strong (soΦ(1− π, 0)−Φ(π, 1) > 0), as otherwise players would react toinformation about the most recent past generation and could changeto High behavior if they had a strong enough signal regarding thepast play and would also expect the next generation to have goodinformation.




Focusing on the greatest equilibrium:Let

γH ≡ (1− λ)Φ(1− π, 0) + λ (1− π) . (20)

Thus relative to γ∗H , more “optimistic”expectations about the future.

Proposition

The greatest equilibrium is such that:

(i) following a prominent play of L, there is a low social norm and allendogenous agents play L if and only if γL < γ; and

(ii) following a prominent play of H, there is a high social norm and allendogenous agents play H if and only if γ ≤ γH .

Thus, endogenous players always follow the play of the most recentprominent player in the greatest equilibrium if and only if γL < γ ≤ γH .



General Characterization of Greatest Equilibrium

LetγH ≡ (1− λ)Φ(1− π, 1) + λ (1− π) .

This is the expectation of (1− λ)φtt−1 + λφtt+1 for an agent whobelieves that any regular agent preceding him or her played H andsees the most optimistic signal, and believes that all subsequentendogenous agents will play H.

Above, this threshold, no regular agent would ever play H.



General Characterization (continued)

Proposition

In the greatest equilibrium:

1 If γ ≤ λ(1− π), then all endogenous agents play H in allcircumstances, and thus society has a stable high behavioral pattern.

2 If λ(1− π) < γ ≤ γH , then following a prominent play of H (butnot following the prominent play of L) all endogenous agents play H.

3 If γL < γ ≤ γH , then following a prominent play of L, all endogenousagents play L, and so all endogenous players follow the play of themost recent exogenous prominent player.

4 If γH < γ, then endogenous agents play L for at least some signals,periods, and types even following a prominent play of H.

5 If γH < γ, then all endogenous agents who do not immediately followa prominent H play L regardless of signals or types.



General Characterization of Greatest Equilibrium(continued)



Reversion of Play

What happens when all High and all Low are not stable social norms?

Answer: play reverts from an extreme (started by a prominent agent)to a steady-state distribution.

Start with HNext player knows previous is H with probability 1Next player knows previous endogenous played H, but this hasprobability 1− π, so action made depend on signal

In fact, even stronger, because she knows that her signals will beinterpreted is not necessarily coming from H .

Next player knows previous play was H with probability < 1− π.



Reversion of Play (continued)




Let us denote the cutoffs used by prominent and non-prominentagents τ periods after the last prominent agent by cPτ and cNτrespectively.

We say that high play decreases over time if (cPτ , cNτ ) ≤ (cPτ+1, cNτ+1)

for each τ.

We say that high play strictly decreases over time, if in addition, wehave that when (cPτ , c

Nτ ) 6= (0, 0), (cPτ , cNτ ) 6= (cPτ+1, cNτ+1).

The concepts of high play increasing and strictly increasing aredefined analogously.




Proposition

1 In the greatest and least equilibria, cutoff sequences(cPτ , c

Nτ

)are

monotone. Thus, following a prominent agent choosing H,(cPτ , c

Nτ

)are nondecreasing and following a prominent agent choosing L, theyare non-increasing.

2 If γ > γH , then in the greatest equilibrium, high play strictlydecreases over time following high play by a prominent agent.

3 If γ < γL, then in the greatest equilibrium, high play strictly increasesover time following low play by a prominent agent.

But important asymmetry from switching from L to H vs from H to LAs we will see next, endogenous prominent agents would not like to thelatter, but would prefer to do the former, so the first type of switchesare driven by both exogenous and endogenous prominent agents, whilethe second only by exogenous prominent agents.




The following is an immediate corollary of Proposition 10.

Corollary

As the distance from the last prominent agent grows (τ → ∞), cutoffs inthe greatest equilibrium converge and the corresponding distributions ofplay converge to a stationary distribution. Following a choice of H by thelast prominent agent, this limiting distribution involves only H by allendogenous agents if and only if γ ≤ γH . Similarly, following a choice of Lby the last prominent agent, this limiting distribution involves L by allendogenous agents if and only if γ ≥ γL.



Leadership: Breaking the Low Social Norm

Can promise breaker social norm of L?

Regular agents may be stuck in L for reasons analyzed so far.But prominence, greater visibility in the future, can enable “leadership”

Idea:

endogenous prominent agents can always break the social normwhen “all L” is not the unique equilibrium after prominent L,endogenous prominent agents will like to break the social norm of Land start a switch to H



Leadership: Breaking the Low Social Norm (continued)

Proposition

1 Suppose that the last prominent agent played L and

γL ≤ γ < γH ≡ (1− λ)Φ (π, 0) + λ (1− π) . (21)

Then there exists a fixed cutoff below 1 (after at least one period)such that an endogenous prominent agent chooses High and breaksthe Low social norm if the signal is above the cutoff.

2 Suppose that γ < γL and γ < γH . Suppose that the last prominentagent has played L. Endogenous prominent agents have cutoffs below1 that decrease with time such that if the signal is above the cutoffthen in a greatest equilibrium the endogenous prominent agent willchoose H and break a low social norm.

3 Moreover, in either case if γ < γ∗H , the above are the uniquecontinuation equilibrium.



Role of Prominence

Prominence provides greater visibility and thus coordinates futureactions.

Crucially: common knowledge of visibility.

Without this, prominence is less effective.



Role of Prominence (continued)

Suppose there is a starting non-prominent agent at time 0 who playsHigh with probability x0 ∈ (0, 1), where x0 is known to all agents whofollow, and generates a signal for the first agent in the usual way.

All agents after time 1 are not prominent.

In every case all agents (including time 1 agents) are endogenous withprobability (1− 2π).

Scenario 1: The agent at time 1 is not prominent and his or her action isobserved with the usual signal structure.Scenario 2: The agent at time 1’s action is observed perfectly by theperiod 2 agent, but not by future agents.Scenario 2′: The agent at time 1 is only observed by the next agentaccording to a signal, but then is subsequently perfectly observed by allagents who follow from time 3 onwards.Scenario 3: The agent at time 1 is prominent, and all later agents areviewed with the usual signal structure.



Role of Prominence (continued)

Clearly, as we move from Scenario 1 to Scenario 2 (or 2′) to Scenario3, we are moving from a non-prominent agent to a prominent one

Let us focus again on the greatest equilibrium and letck (λ,γ, fH , fL, q,π) denote the cutoff signal above which the firstagent (if endogenous) plays High under scenario k as a function ofthe underlying setting.

Proposition

The cutoffs satisfy c2(·) ≥ c3(·) and c1(·) ≥ c2′(·) ≥ c3(·), and thereare settings (λ,γ, fH , fL, q,π) for which all of the inequalities are strict.



Multiple Agents

Now suppose n agents within each generation, and random matching;unless there is a prominent agent, in which case all those fromprevious and next generations match with the prominent agent.

If no prominent agent, then observe a signal generated by the actionof a randomly generated agent from the previous generation.

Results generalize, except but now we can do comparative staticswith respect to n.



Multiple Agents (continued)

Proposition

In the model with n agents within each generation, there exist greatestand least equilibria. In the greatest equilibrium:

1 following a prominent play of Low, there is a Low social norm and allendogenous agents play Low (i.e., σSMτ (a = Low , s,T ) = Low for alls, T and all τ > 0) if and only if γnL < γ; and

2 following a prominent play of High, there is a High social norm andall endogenous agents play High (i.e., σSMτ (a = High, s,T ) = Highfor all s, T and all τ > 0) if and only if γ ≤ γnH .

The threshold γnH is increasing in n and and the threshold γnL is decreasingin n, so that both High and Low social norms following, respectively, Highand Low prominent play, emerge for a larger set of parameter values.

Intuition: signals less informative, thus history matters more.


Culture, Norms and Institutions Collective Action

Collective Action

A model of collective action would be similar, except that interactionswould be between many players rather than just two.

From the New Yorker 2/28/11 quote of an Egyptian student in thecontext of people cleaning up Tahrir square:“We thought people didn’t care and just threw their garbage on thestreet, but now we see that they just thought it was hopeless - whybother when it’s so dirty. Why not be corrupt when everything iscorrupted. But now things have changed, and it’s a different moodovertaking. Even I can’t stop smiling myself.”

Why have things changed?

One interpretation: switches in social norm driven by prominentevents (and the endogenous history that this generates).


Culture, Norms and Institutions Laws and Norms

Laws and Norms

How norms influence institutions? How are they influenced byinstitutions?

A specific context is the interplay between laws and norms:

norms may make laws less effective (e.g., nobody obeys them becausethey conflict with the social norms);laws may change social norms.

A simple model to study these issues: Acemoglu and Jackson (2015).



Static Setup

Finite population of agents, N = {1, . . . , n}, with n ≥ 2 taken to beeven, and much pairwise match pairwise.

Agent i has type θi ∈ [0, 1], distributed according to a cumulativedistribution function F .

Agent i chooses a base behavior bi ∈ [0, 1]The agent’s actual behavior may be forced away from this level expost to some Bi because of the enforcement of a law.



Laws

A law, L ∈ [0, 1], is an upper bound on the behaviors of agents,meaning that any behavior above L is prohibited.

The government detects law-breaking in any pair with probabilityη ∈ [0, 1), but can also find out about law-breaking because ofwhistle-blowing within the partnership.

If a law-breaker is caught, her behavior is brought down to Bi = Land she pays a fine φ.

In particular, an agent i can whistle-blower on her partner m(i) if heis breaking the law, i.e., bm(i ) > L, and she is herself law-abiding, i.e.,bi ≤ L.This last requirement captures the fact that if a law-breakerwhistle-blows, then she may get caught herself and be subject to afine.



Actual Behaviors and Payoffs

The actual behavior of agent i is

Bi(wm(i ), bi

)=

{L if bi > L, and wm(i ) = 1 or if there is public enforcement (probability η)bi otherwise.

Agent i’s payoff is given by

ui (θi ,Bi ) =− a (Bi − θi )2 − (1− a)

(Bi − Bm(i )

)2− ζmBm(i ) − ζo ∑

j 6=i ,m(i )Bj −

(η + (1− η)wm(i )I{bi>L}

)φ.

(22)

The parameters ζm , ζo ≥ 0 capture negative externalities from thebehaviors of others.



Equilibrium

It is a strictly dominant strategy for an agent with bi ≤ L andbm(i ) > L to whistle-blow (because this reduces both the externalityand the mismatch with the partner’s behavior).

Thus just focus on first-stage choice of base behavior and define anequilibrium as a pure-strategy symmetric Bayesian equilibriumdescribed by β : [0, 1]→ [0, 1], with β(θi ) indicating the action takenby type θi .

Proposition

An equilibrium exists, and all equilibria are in monotone strategies and arecharacterized by a threshold θ∗ above which all types break the law andbelow which they obey the law.



Characterization of Equilibrium

Proposition

All equilibria are of the following form. There exists θ∗ ∈ [L, 1] such that

β(θi ) = βabiding(θi ) ≡ min[aθi + (1− a)x , L] if θi < θ∗ (23)

and

β(θi ) = βbreaking(θi ) ≡ aθi + (1− a)E[θ|θ > θ∗] if θi > θ∗, (24)

where x is the unique solution to x = E[min β(θ), L].



Representation of Equilibrium

Full compliance and partial compliance equilibria:



Intuition

Without a law, an agent chose a convex combination of her preferredbehavior given by her type, θi , and expected behavior in society.

For law-abiding agents, the calculus is still similar, except that asshown by the expression, aθi + (1− a)x , the expected behavior isreplaced by x , because she can whistle-blow on a law-breaking partnerand bring his behavior down to L.

On the other hand, a law-breaker knows that his partner, if she islaw-abiding, will whistle-blow on him, setting their behavior down toL. Thus, when choosing their behavior, he will need to reasonconditionally – conditional on matching with another law-breakingagent and not being subject to public enforcement. This is the reasonwhy the term E[θ|θ > θ∗] appears.



Multiple Equilibria

In general there can be multiple equilibria. In particular

Proposition

For any L ∈ (0, 1), there exists φ ≥ 0, such thatif φ > φ, then there is a unique equilibrium, which involves fullcompliance (all types obey the law);

if φ < φ, then there are multiple equilibria: one with full complianceand (at least two) other equilibria ordered by the threshold abovewhich all types break the law.

Intuitively, if others are expected to break the law, they cannotwhistle-blow and breaking the law becomes more attractive.

This captures the fact that the effectiveness of laws is interwovenwith social norms, here corresponding to expected behavior of others.



Comparative Statics

Proposition

Consider the lowest compliance equilibrium. Then:

1 A small increase in φ (higher fine), ζm (greater within-matchexternality), and/or η (higher likelihood of public enforcement):increases θ∗ and so lowers the fraction of agents breaking the law;leaves behavior by each agent who was obeying the law unchanged;but leads to higher behavior among those still breaking the law.

2 There exists ζm > 0 such that if ζm < ζm , a small decrease in L (astricter law): decreases θ∗, increasing the fraction of agents breakingthe law; leads to lower behavior by each agent who was alreadybreaking the law; and leads to lower average behavior by thoseobeying the law.

Note the non-monotonicity in behavior.



Comparative Statics in a Diagram

Nonmonotone behavior the population – greater φ less law-breaking,but greater behavior among law-breakers.



Nonmonotonicity in Average Behavior

Nonmonotonicity in response to tighter laws both because of multipleequilibria and competing effects.



Dynamic Model

Now consider this same set up in the context of an overlappinggenerations model, where each agent plays with a random partnerfrom the previous and next generations (with weights 1− λ and λ onpayoffs from previous and next generations).

The rest of the setup is unchanged.



Dynamic Equilibria

Dynamic equilibria are similar (a little more involved).But steady-state equilibria are identical. In particular:

Proposition

Let B be the set equilibria of the static game, and B∗ be the set ofsteady-state behaviors from the equilibria of the dynamic game (with thesame parameter values as the static game and with Lt = L and φt = φ forall t). Then B = B∗, and every steady-state equilibrium is described by astrategy of the form

β∗(θi ) =

{βabiding(θi ) if θi < θ∗

βbreaking(θi ) if θi > θ∗

for some threshold θ∗, where βabiding(θi ) and βbreaking(θi ) are as defined in(23) and (24) in the static proposition, and then i whistle-blows occurs ifand only if θi < θ∗ and a match breaks the law.



Social Norms and Effectiveness of Laws

Proposition

Fix F , φ > 0 and ζ ≥ 0, let λ = 0, take η and a small, and start withinitial non-binding law (i.e., L ≥ (1− a)E[θ] + a). Suppose that societystarts at time t = 0 in the unique steady-state equilibrium correspondingto L, and consider new law L′ < (1− a)E[θ]− a (so that there is a lessthan full compliance steady-state equilibrium under L′).

(Abrupt tightening of law) If there is an unanticipated and permanentchange to L′ in period 1, then all agents break the law in period 1,and behavior converges to the lowest compliance equilibriumassociated with L′.

(Gradual tightening of law) However, for any such L′ there exists a(finite) decreasing sequence of laws {Lt}Tt=1 with LT = L′ such thatfollowing a switch to this sequence of laws, all agents comply with thelaw at their birth and play converges to the full compliancesteady-state equilibrium associated with L′.



Gradual vs. Abrupt Tightening of Laws



Interpretation

A significant tightening of the law creates a conflict between theprevailing norms and the law, leading to an immediate and significantincrease in law-breaking.This then makes it impossible for society to achieve the fullcompliance steady-state equilibrium.In contrast, a series of gradual laws converging to L′ can be muchmore effective in containing law-breaking and can achieve fullcompliance.In particular, each gradual tightening of the law will have a smallimpact on behavior, and the next generation will be willing to abideby the law, because this enables both coordination with the currentgeneration and avoids the costs imposed by public law enforcement.This gradual sequence of tighter laws slowly changes the prevailingnorms, and as norms change, these tighter laws become more andmore powerful in restricting behavior.



Multiple Behaviors

Now suppose that there are two unrelated types of behaviors,(b1i , b

2i

).

Suppose that types are also two-dimensional, (θ1i , θ2i ), and are

independently drawn.

Thus the only interaction between the two behaviors is thatlaw-breaking on one dimension precludes whistle-blowing.



Equilibria with Multiple Behaviors

Proposition

Consider the model with multiple laws described above. Suppose thatthere is a non-trivial law in the first dimension (L1 < 1) but no law in thesecond dimension (L2 = 1), and an associated equilibrium,

(β1(θ), β2(θ)

)with a law-breaking threshold θ1∗ < 1 on the first dimension. Then:

There exist δ and δ such that if a law L2 ∈ (L1 − δ, L1+ δ) isimposed on the second dimension, then there is a new equilibrium(

β1(θ), β

2(θ))that involves a law-breaking threshold θ

1∗> θ1∗ (i.e.,

there is less law-breaking on the first dimension).

There exists L > 0 such that if a law L2 < L is imposed on the

second dimension, then the new equilibrium(

β1(θ), β

2(θ))involves

a law-breaking threshold θ1∗< θ1∗ (i.e., there will be more

law-breaking on the first dimension).



Interpretation

Bad laws in some dimensions create negative spillovers on law-abidingon all dimensions.

Implications for the “broken windows theory”– the problem may notbe one of enforcement but one of bad laws.

But also at the same time good laws increased law-abiding behavior inother dimensions because individuals now have an incentive to providewith all laws to benefit from the implementation of (reasonable) laws.


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